On Wednesday, the provincial branch released a statement saying Khoza has "crossed the line and must immediately face the consequences of her actions.

"The latest public pronouncements of Khoza represented the worst form of arrogance which is completely at variance with the conduct expected from those representing the ANC."

Defending the statement, ANC KZN spokesman Mdumiseni Ntuli said what was meant was that Khoza needs to be taken to a disciplinary committee so that she can "answer for what appears to be very strange conduct".

"Because she is a member of our association and she is also technically deployed by KZN because she forms part of a list of MPs who were sent from our office, it is our responsibility to act against what appears to be a total disregard for the organisation," Ntuli said.

Parliament, in a statement on Wednesday, said it is working with the police to provide protection for Khoza.

However, after the announcement was made, Khoza took to Facebook, slamming Police Minister Fikile Mbalula for finally condemning the death threats against her -- but only after "fuelling them" himself.

In the post, she said: "The Minister himself [Mbalula] fueled the threats. He also joined those who wanted to eliminate me and have me dismissed or expelled from the ANC for choosing to uphold not just the RSA Constitution but that of the ANC."

Mbalula came out fighting in response on Thursday, saying Khoza had not availed herself for meeting with investigators on her case.

"SAPS (police) also requires that [Khoza] avails herself to the investigating officer who continues to battle to get her to a meeting. [Khoza's] house has also been visited unannounced after SAPS' frustration with her unavailability to meet them," Mbalula said.

"My office's calls to [Khoza] and even those from myself directly have not yielded the result we had hoped for, as it is at this time, she refuses to engage with us directly but through Facebook... If needs be, should [Khoza] refuse our overtures and open hand, we shall look at other ways of assisting her without her involvement should it come to that."

He said the police have found no threat against Khoza's family members.